The present invention relates to an ultrasonic flow meter. In particular, the invention relates to a flow meter using continuous ultrasonic waves.
Flow meters using ultrasonic waves can be classified into two types. That is, one is the flow meter of the ultrasonic pulse system and the other is the flow meter of the continuous ultrasonic wave system.
In a conventional flow meter using ultrasonic pulses, the ultrasonic pulse beam is transmitted into the fluid so that the flow rate is obtained from the propagation time of the pulse in the fluid. In this case, there was a drawback. That is, since the flow rate is measured from the time difference of the pulses, which becomes short when the flow rate is small, it was required that the clock frequency be high (to the limit of IC at present). Thus it was difficult to enlarge and measure small time differences.
In a flow meter using continuous ultrasonic waves, the ultrasonic beam is transmitted into the fluid from the ultrasonic transducer for transmission directly to the ultrasonic transducer for reception provided at another position in the fluid, and the flow rate of the fluid is obtained from the phase difference or another quantity depending on the flow rate.
In the conventional ultrasonic flow meter of either one of the above mentioned types, the ultrasonic wave was transmitted and received as a beam. It was required that the ultrasonic transmitter and the ultrasonic receiver are to be opposite to each other in order that the ultrasonic wave beam is mutually transmitted and received; it was possible to measure the flow rate only at the straight portion of the tube in which the fluid flows.
To improve the accuracy in measurement by making the phase difference or the time difference large, it is preferable that the angle .theta. between the ultrasonic beam and the axis of the tube should be made small to make the time difference long, in other words, the beam is made parallel to the axis of the tube. Since it was also required that the ultrasonic transmitter be opposite to the ultrasonic receiver, the degree of design freedom was limited.
In addition, in order to make the ultrasonic beam sharp, the frequency should be high. When the frequency becomes high, the short range acoustic field AF (=D.sup.2 /4.lambda., wherein D is the diameter of the ultrasonic transducer and .lambda. is the wave length) becomes larger; the length l between the transmitter and the receiver becomes comparable with the short range acoustic field and the side lobe becomes larger, particularly when the diameter of the tube is small. In other words, not only the waves propagated along the straight line connecting the transmitter and the receiver, but also the waves which have propagated in various directions, are received, which increases the beam width and makes it difficult to measure the time difference correctly. These drawbacks were present in the continuous ultrasonic flow meter using the ultrasonic beam in accordance with the piror art.
In order to overcome the above mentioned drawbacks, the present inventor has invented a flow meter using a continuous ultrasonic wave which is not in the form of an ultrasonic beam. The ultrasonic wave is a standing wave in the cross section of the tube and a propagating wave in the axial direction of the tube. It is characteristic that the ultrasonic transducer for transmission and the ultrasonic transducer for reception are arranged on the wall of the tube so as not to be opposite to each other.
The degree of freedom is high in mounting the ultrasonic transducers in this ultrasonic flow meter. It is also possible to measure without disturbing the flow in the tube, because it is possible to mount the ultrasonic transducers on the outside of the wall of the tube. In addition, since it is not necessary to provide any member for causing a vortex as in the Karman vortex flow meter, it is possible to make the pressure loss zero due to the member for causing vortex.
The principle of the measurement of the flow meter in accordance with the present invention is as follows: The ultrasonic wave does not propagate in a form of the ultrasonic beam but propagates as a standing wave in the tube. The propagation of the ultrasonic wave in the fluid follows the wave equation. Since the ultrasonic wave in tube has the limited boundary, the solution of to the equation is different from that in free space, so that the group velocity (acoustic velocity) C of the ultrasonic wave is different from that in free space. The solution to this equation is obtained by a mathematical method which is the same as that for a microwave waveguide.
When the tube has the cross section in the x, y planes and the ultrasonic wave propagates in the z direction, a solution of the wave equation is a standing wave in the x, y planes, being a propagating wave in the z direction. With respect this solution, the group velocity C of the ultrasonic wave, which is a function of the frequency f of the ultrasonic wave, is expressed as follows: wherein f.sub.c is the cut-off frequency. ##EQU1##
And the following formula stands. EQU T.sub.v =L/(C+V)
where L is the distance between the ultrasonic transmitter and the ultrasonic receiver, C is the group velocity of the ultrasonic wave in the fluid, V is the relative velocity of the fluid and the ultrasonic transmitter and T.sub.v is the time necessary for the propagation from the ultrasonic transmitter to the ultrasonic receiver. Therefore, the difference .DELTA.T between the propagation times at V=0 and at V.noteq.0 is expressed as follows. EQU .DELTA.T=L/C-L/(C+V)
The above expression is Taylor-expanded, so as to obtain the following expression. ##EQU2##
In case V&lt;&lt;C, .DELTA.T is proportional to V, .DELTA.T=LV/C.sup.2. Thus, it is possible to obtain the flow rate V from .DELTA.T, C and l.
It is to be noted that the time difference .DELTA.T may be obtained from the phase difference of the ultrasonic waves. Suppose the frequency of the ultrasonic wave is f, the phase difference .phi. which corresponds to the time difference .DELTA.T satisfies the following relationship. EQU cos .phi.=cos 2.pi.f.DELTA.T
When 0.ltoreq..phi..ltoreq..pi., the following expression stands. EQU .phi.=2.pi.f.DELTA.T=2.pi.fLV/C.sup.2
Thus it is possible to obtain the flow rate V by detecting the phase difference .phi..
In obtaining the flow rate V from the time difference .DELTA.T, the group velocity (acoustic velocity) C and the distance L, the measurement has the following difficulties.
(i) In obtaining the flow rate V from the phase difference .DELTA..phi., the available phase difference range is 0-.pi.. Therefore, it is impossible to enlarge the range of the measurable flow rate.
(ii) The variance of the acoustic velocity in the fluid is a cause of error in measuring the flow rate, since the acoustic velocity C of the ultrasonic wave in the fluid depends upon the temperature of the fluid.